Question

4) Order the following functions by growth rate. Indicate which functions grow at the same rate (15 points) N, N2, log N, N log N, log(N2), log2 N, N log2N, 2, 2N, 37, N2 log N, 5logN, N3, 10N log N2

Needs to be explained also, like what method you used to compare the growth rate. Thank you

Answer 1

Hey,

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The order is

2 and 37 both are O(1)

log(N^2)=2log(N)

So, log(N^2) and log(N) and 5log(N) since constant in multiplication doesn't affect order. So, both are order log(N)

(log(N))^2>log(N) Since log(N)>constant

Exponential is the biggest of all

2=37<log(N)=log(N^2)=5log(n)<(log(N))^2<N<Nlog(N)=10N*log(N^2)<N*(log(N))^2<N^2<N^2log(N)<N^3<2^N

Kindly revert for any queries

Thanks.